speclib.f90 File Reference

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Modules
module	speclib
	LIBRARY ROUTINES FOR SPECTRAL METHODS.

Functions/Subroutines
subroutine	speclib::zwgl (z, w, np)
	Generate NP Gauss Legendre points Z and weights W associated with Jacobi polynomial \( P(N)(\alpha=0, \beta=0) \). The polynomial degree N = NP-1.
subroutine	speclib::zwgll (z, w, np)
	Generate NP Gauss-Lobatto Legendre points (Z) and weights (W) associated with Jacobi polynomial P(N)(alpha=0,beta=0). The polynomial degree N=NP-1. Z and W are in single precision, but all the arithmetic operations are done in double precision.
subroutine	speclib::zwgj (z, w, np, alpha, beta)
	Generate NP GAUSS JACOBI points (Z) and weights (W) associated with Jacobi polynomial P(N)(alpha>-1,beta>-1). The polynomial degree N=NP-1. Single precision version.
subroutine	speclib::zwgjd (z, w, np, alpha, beta)
	Generate NP GAUSS JACOBI points (Z) and weights (W) associated with Jacobi polynomial P(N)(alpha>-1,beta>-1). The polynomial degree N=NP-1. Double precision version.
subroutine	speclib::zwglj (z, w, np, alpha, beta)
	Generate NP GAUSS LOBATTO JACOBI points (Z) and weights (W) associated with Jacobi polynomial P(N)(alpha>-1,beta>-1). The polynomial degree N=NP-1. Single precision version.
subroutine	speclib::zwgljd (z, w, np, alpha, beta)
	Generate NP GAUSS LOBATTO JACOBI points (Z) and weights (W) associated with Jacobi polynomial P(N)(alpha>-1,beta>-1). The polynomial degree N=NP-1. Double precision version.
real(kind=xp) function	speclib::endw1 (n, alpha, beta)
real(kind=xp) function	speclib::endw2 (n, alpha, beta)
real(kind=xp) function	speclib::gammaf (x)
real(kind=xp) function	speclib::pnormj (n, alpha, beta)
subroutine	speclib::jacg (xjac, np, alpha, beta)
	Compute NP Gauss points XJAC, which are the zeros of the Jacobi polynomial J(NP) with parameters ALPHA and BETA. ALPHA and BETA determines the specific type of Gauss points. Examples: ALPHA = BETA = 0.0 -> Legendre points ALPHA = BETA = -0.5 -> Chebyshev points.
subroutine	speclib::jacobf (poly, pder, polym1, pderm1, polym2, pderm2, n, alp, bet, x)
	Computes the Jacobi polynomial (POLY) and its derivative (PDER) of degree N at X.
real(kind=xp) function	speclib::hgj (ii, z, zgj, np, alpha, beta)
	Compute the value of the Lagrangian interpolant HGJ through the NP Gauss Jacobi points ZGJ at the point Z. Single precision version.
real(kind=xp) function	speclib::hgjd (ii, z, zgj, np, alpha, beta)
	Compute the value of the Lagrangian interpolant HGJD through the NZ Gauss-Lobatto Jacobi points ZGJ at the point Z. Double precision version.
real(kind=xp) function	speclib::hglj (ii, z, zglj, np, alpha, beta)
	Compute the value of the Lagrangian interpolant HGLJ through the NZ Gauss-Lobatto Jacobi points ZGLJ at the point Z. Single precision version.
real(kind=xp) function	speclib::hgljd (i, z, zglj, np, alpha, beta)
	Compute the value of the Lagrangian interpolant HGLJD through the NZ Gauss-Lobatto Jacobi points ZJACL at the point Z. Double precision version.
subroutine	speclib::dgj (d, dt, z, nz, nzd, alpha, beta)
	Compute the derivative matrix D and its transpose DT associated with the Nth order Lagrangian interpolants through the NZ Gauss Jacobi points Z. Note: D and DT are square matrices. Single precision version.
subroutine	speclib::dgjd (d, dt, z, nz, nzd, alpha, beta)
	Compute the derivative matrix D and its transpose DT associated with the Nth order Lagrangian interpolants through the NZ Gauss Jacobi points Z. Note: D and DT are square matrices. Double precision version.
subroutine	speclib::dglj (d, dt, z, nz, nzd, alpha, beta)
	Compute the derivative matrix D and its transpose DT associated with the Nth order Lagrangian interpolants through the NZ Gauss-Lobatto Jacobi points Z. Note: D and DT are square matrices. Single precision version.
subroutine	speclib::dgljd (d, dt, z, nz, nzd, alpha, beta)
	Compute the derivative matrix D and its transpose DT associated with the Nth order Lagrangian interpolants through the NZ Gauss-Lobatto Jacobi points Z. Note: D and DT are square matrices. Double precision version.
subroutine	speclib::dgll (d, dt, z, nz, nzd)
	Compute the derivative matrix D and its transpose DT associated with the Nth order Lagrangian interpolants through the NZ Gauss-Lobatto Legendre points Z. Note: D and DT are square matrices.
real(kind=xp) function	speclib::hgll (i, z, zgll, nz)
	Compute the value of the Lagrangian interpolant L through the NZ Gauss-Lobatto Legendre points ZGLL at the point Z.
real(kind=xp) function	speclib::hgl (i, z, zgl, nz)
	Compute the value of the Lagrangian interpolant HGL through the NZ Gauss Legendre points ZGL at the point Z.
real(kind=xp) function	speclib::pnleg (z, n)
	Compute the value of the Nth order Legendre polynomial at Z. (Simpler than JACOBF) Based on the recursion formula for the Legendre polynomials.
subroutine	speclib::legendre_poly (l, x, n)
	Evaluate Legendre polynomials of degrees 0-N at point x and store in array L.
real(kind=xp) function	speclib::pndleg (z, n)
	Compute the derivative of the Nth order Legendre polynomial at Z. (Simpler than JACOBF) Based on the recursion formula for the Legendre polynomials.
subroutine	speclib::dgllgl (d, dt, zm1, zm2, im12, nzm1, nzm2, nd1, nd2)
	Compute the (one-dimensional) derivative matrix D and its transpose DT associated with taking the derivative of a variable expanded on a Gauss-Lobatto Legendre mesh (M1), and evaluate its derivative on a Guass Legendre mesh (M2). Need the one-dimensional interpolation operator IM12 (see subroutine IGLLGL). Note: D and DT are rectangular matrices.
subroutine	speclib::dgljgj (d, dt, zgl, zg, iglg, npgl, npg, nd1, nd2, alpha, beta)
	Compute the (one-dimensional) derivative matrix D and its transpose DT associated with taking the derivative of a variable expanded on a Gauss-Lobatto Jacobi mesh (M1), and evaluate its derivative on a Guass Jacobi mesh (M2). Need the one-dimensional interpolation operator IM12 (see subroutine IGLJGJ). Note: D and DT are rectangular matrices. Single precision version.
subroutine	speclib::dgljgjd (d, dt, zgl, zg, iglg, npgl, npg, nd1, nd2, alpha, beta)
	Compute the (one-dimensional) derivative matrix D and its transpose DT associated with taking the derivative of a variable expanded on a Gauss-Lobatto Jacobi mesh (M1), and evaluate its derivative on a Guass Jacobi mesh (M2). Need the one-dimensional interpolation operator IM12 (see subroutine IGLJGJ). Note: D and DT are rectangular matrices. Double precision version.
subroutine	speclib::iglm (i12, it12, z1, z2, nz1, nz2, nd1, nd2)
	Compute the one-dimensional interpolation operator (matrix) I12 ands its transpose IT12 for interpolating a variable from a Gauss Legendre mesh (1) to a another mesh M (2). Z1 : NZ1 Gauss Legendre points. Z2 : NZ2 points on mesh M.
subroutine	speclib::igllm (i12, it12, z1, z2, nz1, nz2, nd1, nd2)
	Compute the one-dimensional interpolation operator (matrix) I12 ands its transpose IT12 for interpolating a variable from a Gauss-Lobatto Legendre mesh (1) to a another mesh M (2). Z1 : NZ1 Gauss-Lobatto Legendre points. Z2 : NZ2 points on mesh M.
subroutine	speclib::igjm (i12, it12, z1, z2, nz1, nz2, nd1, nd2, alpha, beta)
	Compute the one-dimensional interpolation operator (matrix) I12 ands its transpose IT12 for interpolating a variable from a Gauss Jacobi mesh (1) to a another mesh M (2). Z1 : NZ1 Gauss Jacobi points. Z2 : NZ2 points on mesh M. Single precision version.
subroutine	speclib::igljm (i12, it12, z1, z2, nz1, nz2, nd1, nd2, alpha, beta)
	Compute the one-dimensional interpolation operator (matrix) I12 ands its transpose IT12 for interpolating a variable from a Gauss-Lobatto Jacobi mesh (1) to a another mesh M (2). Z1 : NZ1 Gauss-Lobatto Jacobi points. Z2 : NZ2 points on mesh M. Single precision version.